Comput. Sci. Math. Forum, 2023, IOCMA 2023

The three-dimensional problem of the modelling of elastic wave propagation in a multi-layered acoustic metamaterial, a periodic elastic composite with periodic arrays of interface cracks or planar voids of arbitrary shape, is considered. The boundary integral equation method is extended for this purpose. The unknown crack-opening displacement vectors for each array are related using the Floquet theorem and solved using the Galerkin method at reference delaminations in the arrays. The developed method provides an efficient tool for fast parametric analysis of the influence of the periodic crack array characteristics on the transmission and diffraction of elastic waves. Two modifications to the boundary integral equation method are proposed and compared for rectangular cracks. To reduce computational costs, a preliminary analytical evaluation of the arising integral representations in terms of the Fourier transform of Green’s matrices and the crack-opening displacements are presented. Full article

Valuation theory is an important area of investigation in algebra, with applications in algebraic geometry and number theory. In 1957, M. Krasner introduced hyperfields, which are field-like objects with a multivalued addition, to describe some structures arising naturally from valued fields. We wish to discuss the possibility of generalising the notion of valuation to the multivalued setting and the potential that this higher point of view has in the understanding of classical valuation theory. We will see that a valuation on a field K is nothing but a homomorphism of hyperfields from K onto a special type of hyperfield, which we call a (generalised) tropical hyperfield. Full article

The differential entropy of a continuous waveform is defined over the period spanned by the recording. The time-dependent information dynamics of the observed process are not accessible to this measure. We review here the construction and validation of approximate time-dependent measures of information dynamics. Full article

The spread of the respiratory viral infections is currently being widely investigated, and the influence of the immune response on the spread of these infections is of particular interest. In this work, the set of hierarchical models for the spread of infection with respect to the immune response is formulated and analysed. The models are based on the one-dimensional reaction-diffusion equations, and they are investigated both numerically and analytically. For these models, the speed of the wave propagation and the total viral load are evaluated, and their dependencies on the parameters characterizing the intensity of the innate and adaptive immune response are defined. These results show that more intense immune response leads to the small infectivity and severity of the decrease. Different parts of the immune response influence the infectivity and severity of the disease in different ways. These dependencies can help in planning of the treatment strategy. Full article

The decision-making process is of utmost importance as it dictates what will be chosen. Good decision making may lead to an ideal result that decision makers wish to achieve. Decision-making process is an essential consideration for the organization and investors before making decisions. Proper and thorough planning can help the investors make good decisions and, hence, gain profits. As a result, it is important to conduct a financial distress analysis of companies in order to understand their financial condition. In this study, the financial performance of technology companies is assessed using the Grover model. Financial ratios, such as working capital to total assets, earnings before interest and taxes to total assets, and net income to total assets, are analyzed in this study with the Grover model. Each of the companies will obtain a G-score based on their financial performance. The Grover model is capable of categorizing companies either in safe, grey or distress zones. The findings of this paper depict that 28 companies are performing well during the period of study. It indicates that these companies are performing well in terms of financial performance. Therefore, this provides insights to investors to identify companies with good financial performance for investment. Furthermore, the identified companies in the safe zone can serve as a reference to other companies for benchmarking. Full article

Obtaining an approximation for the majority of sparse linear systems found in engineering and applied sciences requires efficient iteration approaches. Solving such linear systems using iterative techniques is possible, but the number of iterations is high. To acquire approximate solutions with rapid convergence, the need arises to redesign or make changes to the current approaches. In this study, a modified approach, termed the “third refinement” of the Gauss–Seidel algorithm, for solving linear systems is proposed. The primary objective of this research is to optimize for convergence speed by reducing the number of iterations and the spectral radius. Decomposing the coefficient matrix using a standard splitting strategy and performing an interpolation operation on the resulting simpler matrices led to the development of the proposed method. We investigated and established the convergence of the proposed accelerated technique for some classes of matrices. The efficiency of the proposed technique was examined numerically, and the findings revealed a substantial enhancement over its previous modifications. Full article

Buy-low-sell-high is one of the basic rules of thumb used by individuals for investment, although it is not considered to be a constructive strategy. In this paper, we show how the appropriate representation of a minute-by-minute trading time series through ordinal (i.e., permutation) patterns and the use of a simple decision heuristic may surprisingly result in significant benefits. We do not compare our proposed approach to sophisticated methods in trading but show how a mathematical model adhering to the idea of bounded rationality may result in significant benefits. Full article

The strong approximation of a function is a useful tool to analyze the convergence of its Fourier series. It is based on the summability techniques. However, unlike matrix summability methods, it uses non-linear methods to derive an auxiliary sequence using approximation errors generated by the series under analysis. In this paper, we give some direct results on the strong means of Fourier series of functions in generalized Hölder and Zygmund spaces. To elaborate its use, we deduce some corollaries. Full article

Machine learning applications usually become a subject of data unavailability, complexity, and drift, resulting from massive and rapid changes in data volume, velocity, and variety (3V). Recent advances in deep learning have brought many improvements to the field, providing generative modeling, nonlinear abstractions, and adaptive learning to address these challenges. In fact, deep learning aims to learn from representations that provide a consistent abstraction of the original feature space, which makes it more meaningful and less complex. However, data complexity related to different distortions, such as higher levels of noise, remains difficult to overcome. In this context, recurrent expansion (RE) algorithms have recently been developed to explore deeper representations than ordinary deep networks, providing further improvement in feature mapping. Unlike traditional deep learning, which extracts meaningful representations through inputs abstraction, RE enables entire deep networks to be merged into another one consecutively, allowing the exploration of inputs, maps, and estimated targets (IMTs) as primary sources of learning; three sources of information that provide additional knowledge about their interactions in a deep network. In addition, RE makes it possible to study IMTs of several networks and learn significant features, improving its accuracy with each round. In this context, this paper presents a general overview of RE, its main learning rules, advantages, disadvantages, and its future opportunities, while reviewing the state-of the art and providing some illustrative examples. Full article

The goal of the present work is to estimate the nonlinear correlation between two random variables when the sample is drawn from a Farlie–Gumbel–Morgenstern (FGM)-type bivariate gamma distribution. In the context of estimating the dependence parameter, a maximum likelihood (ML) methodology is used. Thus, the present work offers ML estimators based on simple random sampling (SRS) and ranked set sampling (RSS). Additionally, we consider generalized modified RSS (GMRSS), which only requires a single rank to obtain a sample. Using GMRSS, we aim to observe the effect of the rth order statistic and its concomitant on the ML estimator. According to the Monte Carlo simulation, it is clearly seen that RSS provides an ML estimator as efficient as the ML estimator based on SRS. On the other hand, it appears that the ML estimator based on GMRSS (with minimum or maximum ranked pairs) is the best option among the studied ML estimators. Moreover, these findings are made even more meaningful by the fact that GMRSS is easier to obtain than SRS and RSS. Full article

The efficient compiling of arbitrary single-qubit gates into a sequence of gates from a finite gate set is of fundamental importance in quantum computation. The exact bounds of this compilation are given by the Solovay–Kitaev theorem, which serves as a powerful tool in compiling quantum algorithms that require many qubits. However, the inverse closure condition it imposes on the gate set adds a certain complexity to the experimental compilation, making the process less efficient. This was recently resolved by a version of the Solovay–Kitaev theorem for inverse-free gate sets, yielding a significant gain. Considering the recent progress in the field of three-level quantum systems, in which qubits are replaced by qutrits, it is possible to achieve the quantum speedup guaranteed by the Solovay–Kitaev theorem simply from orthogonal gates. Nevertheless, it has not been investigated previously whether the condition of inverse closure can be relaxed for these qutrit-based orthogonal compilations as well. In this work, we answer this positively, by obtaining improved Solovay–Kitaev approximations to an arbitrary orthogonal qutrit gate, with an accuracy $\epsilon$ from a sequence of $O\left(lo{g}^{8.62}(1/\epsilon )\right)$ orthogonal gates taken from an inverse-free set. Full article

Deep learning has become widely used in image analysis. Transfer learning can make use of information from other datasets for the analysis of the chosen dataset. When there is a small number of images at hand, transfer learning using pre-trained models with coefficients already estimated from other datasets is recommended. This is in contrast to deep learning, where most model parameters are re-estimated. Deep transfer learning uses pre-trained models with fixed weight parameters in the lower layers; thus, deep learning can be viewed as a two-stage approach: (1) feature extraction from a lower neural network layer and (2) estimation of a neural network using the extracted features as inputs. Since deep transfer learning is feature extraction, we can extend the two-stage approach to a more general two-stage framework: (1) feature extraction using multiple methods and (2) machine learning methods taking extracted features as inputs. We evaluate the performance of methods with different Stage 1 and Stage 2 approaches in predicting the phenotype leaf numbers based on a multi-view plant imaging dataset. This paper contains an evaluation of different two-stage machine learning methods for multi-view image data in plant image phenotyping. Full article

A function is non-differentiable when there is a cusp or a corner point in its graph. To solve this problem, we propose a nonlinear optimization model whose objective function is the Euclidean distance function. To identify the maximum points of a function that has corner or cusp points, according to the proposed model, a series of segments are generated which are measured through the Euclidean distance, which are all perpendicular to the abscissa axis. Therefore, by maximizing the Euclidean distance, it is possible to identify the segment whose points represent the maximum of the function and its projection on the abscissa axis. The proposed model therefore could be an alternative to maximum point search methods in the presence of functions that have points of non-derivability. Full article

In this paper, the effects of various fluid properties on two-dimensional unsteady biomagnetic fluid flow (blood) and heat transfer over a stretching sheet under the appearance of a magnetic dipole is investigated. The governing boundary layer equations are simplified via suitable transformation which are then solved using the bvp4c function approach in MATLAB software. The results indicate that fluid velocity and temperature are greatly influenced by the ferromagnetic interaction parameter. With increasing ferromagnetic number, fluid velocity drops but temperature increases. It is also found that the coefficient of skin friction and Nusselt number increase with an increase in values of thermal conductivity parameter. For certain parameter values, the results are also compared with previously published studies and they are found to be in acceptable agreement. Full article

In this paper, we propose a non-parametric estimator of the conditional hazard function weighted on the recursive kernel method given an explanatory variable taking values in a semi-metric space when the scalar response is censored. Under the ergodicity condition, we establish the convergence rate of this estimator. Full article

In order to generalise semi-invariant Riemannian maps, Sahin first introduced the idea of “Generic Riemannian maps”. We extend the idea of generic Riemannian maps to the case in which the total manifold is a nearly Kaehler manifold. We study the integrability conditions for the horizontal distribution although vertical distribution is always integrable. We also study the geometry of foliations of two distributions and obtain the necessary and sufficient condition for generic Riemannian maps to be totally geodesic. Additionally, we study the generic Riemannian map with umbilical fibers. Full article

In this paper, we study the laminar, incompressible, and steady flow of a biomagnetic fluid, such as blood, containing gold nanoparticles through a shrinking sheet in the presence of a magnetic dipole. This model is consistent with both the principles of magnetohydrodynamics (MHD) and ferro-hydrodynamics (FHD). An effective numerical method that is based on an iterative process, tridiagonal matrix manipulation, and a common finite difference method with central differencing is used to generate the numerical solution of obtained ordinary differential equations (ODEs). The major numerical results show that the fluid velocity decreases as the ferromagnetic number increases whereas the skin friction coefficient shows the opposite behavior. As the ferromagnetic number increases, the rate of heat transfer with ferromagnetic interaction parameter is likewise observed and shown to be decreasing. Full article

Different sports have different fan bases. In addition to this, there is a lot of craze, enthusiasm, and zeal among people, mainly youngsters. Cricket is one among them that has tremendous popularity not only among youngsters, but among all age groups. This creates a kind of pressure among team members to perform well in every game, as well as on the selectors to select the best players for the opening, middle orders, wicketkeeping, and bowling from the pool of players. A game cannot be won by a single player or by openers, among others; rather, it is a collective effort of all the members of the team. As such, it is necessary and one of the most important tasks to choose the players wisely so that they play well in their respective position. In this study, we try to formulate a model using MCDM (multicriteria decision-making techniques), which evaluates not only the performance of the players, but also the performance of different sets (i.e., openers, middle orders, wicket-keepers, and bowlers). For this, we propose a novel ANP-DEA (analytic network process–data envelopment analysis) technique and evaluate the best and worst performing set and their performance evaluation. A case study is conducted to properly visualize the proposed model. Full article

In this work, a novel generalized family of distributions called the odd beta prime is introduced. The linear representations of the proposed family are obtained. The expressions for the moments, the moment-generating function, and entropy are derived. A three-parameter special sub-model of the proposed family called the odd beta prime exponential distribution is proposed. Finally, two real data sets are used to illustrate the usefulness and flexibility of the proposed distribution. Full article

Alexander Grothendieck suggested creating a new branch of topology, called “topologie modérée”. In a paper by N. A’Campo, L. Ji, and A. Papadopoulos the authors conclude that no such tame topology has been developed at a purely topological level. We see our theory of sets with distinguished families of subsets, which we call smopologies, as realising Grothendieck’s idea and the demands of the mentioned paper. Dropping the requirement of stability under infinite unions makes it possible to obtain several equivalences of categories of spaces with categories of lattices. We show several variations in Stone duality and Esakia duality for categories of small or locally small spaces and some subclasses of strictly continuous (or bouned continuous) mappings. Such equivalences are better than the spectral reflector functor for usual topological spaces. Some spectralifications of Kolmogorov locally small spaces can be obtained by Stone duality. Small spaces or locally small spaces seem to be generalised topological spaces. However, looking at them as topological spaces with an additional structure is better. The language of smopologies and bounded continuous mappings simplifies the language of certain Grothendieck sites and permits us to glue together infinite families of definable sets in structures with topologies, which was important when developing the o-minimal homotopy theory. Full article

This article aims to create commutative hyperstructures, starting with a non-commutative group. Therefore, we consider the starting group to be the dihedral group $D_n$, where n is a natural number, $n>1$, and we determine the HX groups associated with the dihedral group. For a fixed number n, we note ${\mathcal{G}}_n=\left\{{\mathcal{G}}_{p_2}^{p_1}HX-\mathrm{groups},\mathrm{for}\mathrm{any}{p}_1,p_2\in {\mathbb{N}}^{*}\mathrm{such}\mathrm{that}n=p_1{p}_2\right\}$ as the set of all HX groups. This paper analyses this new structure’s properties for particular cases when the dihedral group $D_4$ is the support group. Full article

Research on Fe₃O₄/water nano liquid in a lid-driven chamber under mixed convection conditions has been carried out with a focus on the impact of a non-uniform magnetic field on the heat exchange process. The governing equations were resolved using the finite-volume-method-based in-house solver. Several parameters were considered in the analysis, including the magnetic number and the Reynolds number. According to the primary findings, the existence of a magnetic field (MF) generates a region of recirculation near the magnetic source, resulting in improved local heat exchange. Moreover, the effectiveness of the magnetic field is greater at lower Richardson numbers, and the buoyancy force diminishes the influence of the magnetic source. Full article

This paper discusses the relationship between Mock-Lie algebras, Lie algebras, and Jordan algebras. It highlights the importance of the Yang–Baxter equation and symplectic forms in the study of integrable systems, quantum groups, and topological quantum field theory. The paper also proposes studying the admissible associative Yang–Baxter equation in algebras and characterizing Q-Admissible Solutions of the Associative Yang–Baxter Equation in Rota–Baxter Algebras. Finally, it discusses the interplay of coalgebra, r-matrix, and pseudo-Euclidean forms in the context of Jordan algebras and its applications in quantum groups and integrable systems. Full article

Determining the isothermal and adiabatic nonlinearity parameters of liquids and soft matter is crucially important for a variety of engineering applications requiring operations under high pressures, nondestructive testing, exploring the propagation of finite amplitude and shock waves, etc. It has been shown recently that mathematically this problem can be reduced to the initial value problem for an ODE build based on the linear response theory for thermodynamic equalities. The required initial conditions should be determined from thermodynamic measurements at ambient pressure (or along the saturation curve). From the physical point of view, the required regression leading to the determining nonlinearity parameters originates from certain regularities in the response of molecular oscillations to the density changes. In this work, we explore how this regression procedure should be optimized computationally with respect to temperature ranges, which exclude anomalies affecting parameters of equations used for the required predictive calculations under high pressures. The validity of the proposed approach is tested by case studies of the propagation of weakly non-linear waves with finite amplitudes and density changes due to shock waves under the Rankine–Hugoniot jump conditions. Full article

The aim of this paper is to review the most important properties and applications of the complete hypergroups. We will focus on the reversibility, regularity and reducibility properties, on the class equation and the commutativity degree of the complete hypergroups, as well as on the Euler’s totient function defined in this kind of hypergroups. Full article

Today, mathematics teachers are realizing that there are many benefits of problem-driven teaching, but also face a number of challenges, such as a lack of confidence, not knowing how to design high-quality problems, and not knowing how to deal with the challenges that emerge in problem-driven lessons and statistics classes. To address these challenges, we propose a model for problem-driven teaching which includes three stages: the preparation of the problems; the implementation of teaching; and the evaluation and reflection. Accordingly, we select the topic of ’Estimating the population from a sample’ in the General Senior Secondary Textbook, Mathematics, Compulsory Book 2, to design problem-driven instruction and as an application of problem posing. In the instruction, we pose several interesting problems related to the topic. These problems can successfully stimulate students’ interest in learning statistics. Through these problems, the mathematics teacher can guide the students to think actively and to pose and solve the problem themselves, thus understanding the related concepts and methods in statistics. In addition, the design model applied here is a ready-to-use tool for teachers in designing specifically problem-driven instruction, and can also improve teachers’ problem-posing skills. Full article

A relevant problem in combinatorial mathematics is the problem of counting independent sets of a graph G, denoted by $i\left(G\right)$. This problem has many applications in combinatorics, physics, chemistry and computer science. For example, in statistical physics, the computation of $i\left(G\right)$ has been useful in studying the behavior of the particles of a gas on a space modeled by a grid structure. Regarding hard counting problems, the computation of $i\left(G\right)$ for a graph G has been key to determining the frontier between efficient counting and intractable counting procedures. In this article, a novel algorithm for counting independent sets on grid-like structures is presented. We propose a novel algorithm for the computation of $i\left(G_{m,n}\right)$ for a grid graph with m rows and n columns based on the ‘Branch and Bound’ design technique. The splitting rule in our proposal is based on the well-known vertex reduction rule. The vertex in any subgraph from $G_{m,n}$, which is to be selected for the reduction rule, must have four internal incident faces. The ramification process is used to build a computation tree. Our proposal consists of decomposing the initial grid graph until outerplanar graphs are obtained as the ‘basic subgrids’ associated with the leave nodes of the computation tree. The resulting time-complexity of our proposal is inferior to the time-complexity of other classic methods, such as the transfer matrix method. Full article

Financial management is important for the construction sector, as construction companies contribute to the development of countries. Malaysia encourages the construction sector to develop advanced infrastructure related to transport and housing. Financial management is a multi-criteria decision making (MCDM) problem, since companies have to consider multiple goals in order to make the optimal decision. Therefore, goal programming is proposed in financial management to solve optimization in MCDM problems. According to previous studies, there has been no comprehensive study conducted on optimization and comparison among the construction companies with a goal programming model. Thus, this study aims to propose a goal programming model to optimize and compare the financial management of listed construction companies in Malaysia for benchmarking purposes. Six goals of financial management, namely the total assets, total liabilities, equity, profit, earnings, and optimum management of construction companies are examined in this study. The results of this study show that the goal programming model is able to determine the optimal solution and goal achievement for each construction company. In addition, the model value can be further enhanced according to the optimal solution of the goal programming model. This study provides insights to the listed construction companies in Malaysia to identify the potential improvement based on the benchmarking and optimal solution of the goal programming model. Full article

COVID-19 is one of the worst pandemics ever; it is spreading rapidly and creating a health crisis around the world. This disease continues to seriously threaten human life and has caused more than 759 million infections and over 6.8 million deaths worldwide. In this work, we propose a discrete mathematical model of COVID-19 to predict the evolution of the dynamics of this pandemic. We calculate the basic reproduction number and the equilibrium points, and then perform the stability analysis theoretically and numerically. Finally, we conclude with local sensitivity analysis. Full article

The well-known narrow and intense optical absorption J-band was discovered experimentally by Jelley and independently Scheibe in 1936. In 1938, Franck and Teller, associating the appearance of the J-band with the formation of molecular J-aggregates, gave a theoretical explanation for the J-band based on the Frenkel exciton model. This explanation has been developed in detail over a long period of time by many authors, including the author of this paper. The main shortcoming of all those explanations is the inability to explain the shape of the dye monomer bands from which J-aggregates are formed. In this mini-review, the author gives an explanation of the J-band as the so-called Egorov nano-resonance discovered in a new theory, quantum–classical mechanics, which includes an explanation of the shape of monomer bands. Full article

The univariate Topp–Leone distribution introduced by with closed forms of the cumulative distribution function, i.e., [0, 1], was extended to an unbounded limit called the log-Topp–Leone distribution, where the shapes of the hazard function can increase, decrease or remain constant; therefore, this distribution can serve as an alternative distribution to the gamma, Weibull and exponential distributions. The bivariate form of this proposed distribution was introduced by joining the probability density function using three distinct copulas. The MLE, IFM and Bayesian estimation methods were employed to estimate the parameters. The Plackett copula was the best when using the MLE and IFM estimation methods, while the Clayton copula was the best when using the Bayesian method. Full article

In this work, we study the existence and uniqueness of the solution to a wave equation with dynamic Wentztell-type boundary conditions on a part of the boundary ${\Gamma }_1$ of the domain $\Omega$ with non-linear delays in non-linear dampings in $\Omega$ and on ${\Gamma }_1$, using the Faedo–Galerkin method. Full article

In this work, we study stochastic boundary value problems that arise in acoustics and linear elasticity via a Wiener chaos expansion. In particular, for both cases, we provide the appropriate variational formulation for the stochastic-source Helmholtz equation, as well as for the Navier equation with stochastic boundary data. The main idea is to reduce our stochastic problems into an infinite hierarchy of deterministic boundary value problems, for each of which an appropriate variational formulation is considered. Furthermore, we present well-posedness for the above hierarchy of deterministic problems, we give the appropriate linchpin frame with the stochastic problem and we exploit uniqueness and existence arguments for the weighted Wiener chaos solution. Finally, some useful remarks and conclusions are also given. Full article

The aim of this research is to generalize the famous Lyapunov Theorem of the classical explicit differential systems given by two abstract forms: $x^{\prime }\left(t\right)=Px\left(t\right)$ and $x_{n+1}=P{x}_n$ where P is a linear operator, or a matrix when the space has finite dimension in order to study the spectrum of a degenerate differential system. We also use some properties of the spectral theory for the corresponding pencil and an appropriate conformal mapping. The achieved results can be applied to study the stability and controllability of those degenerate systems. Full article

The chaotic dynamics of the transient state in molecular and physicochemical transitions in quantum–classical mechanics is considered in relation to the problem of redistribution of the vibrational–rotational energy of polyatomic molecules M and M₁ in their pairwise collisions based on microcanonical distribution. The statistical (canonical) distribution of the probability of energy change due to collisions in the case of a small impurity M in an equilibrium medium of M₁ is obtained, as well as all of the moments n of this distribution, which, under the conditions of applicability of the semiclassical approximation for the density of vibrational–rotational states, are some polynomials of the n-th order. The theory is compared with experimental data on monomolecular reactions under low pressures for NO₂Cl, C₂H₅NC, and C₅H₁₀ molecules in various gas phase media. Full article

In this paper, we use the concept of measure of nocompactness and fixed-point theorems to investigate the existence and stability of solutions of a class of Hadamard–Stieltjes fractional differential inclusions in an appropriate Banach space, and these results are proven under sufficient hypotheses. We also give an example to illustrate the obtained results. Full article

Forecasting and modeling time series is a crucial aspect of economic research for academics and business practitioners. The ability to predict the direction of stock prices is vital for creating an investment plan or determining the optimal time to make a trade. However, market movements can be complex to predict, non-linear, and chaotic, making it difficult to forecast their evolution. In this paper, we investigate modeling and forecasting the daily prices of the new Morocco Stock Index 20 (MSI 20). To this end, we propose a comparative study between the results obtained from the application of the various Machine Learning (ML) methods: Support Vector Regression (SVR), eXtreme Gradient Boosting (XGBoost), Multilayer Perceptron (MLP), and Long Short-Term Memory (LSTM) models. The results show that using the Grid Search (GS) optimization algorithm, the SVR and MLP models outperform the other models and achieve high accuracy in forecasting daily prices. Full article

The optimal allocation of limited resources along with output target setting are critical in pursuing the sustainability and competitiveness of organizations. The process of resource distribution is usually implemented through a central unit that routes resources to the subordinate decision-making units (DMUs) along with DMUs lower bounds of desired efficiency. Moreover, the central unit has the authority to set the overall expected output targets so as to maximize organizational effectiveness. In this paper, we tackle evaluation efficiency questions using a type of bilevel network data envelopment analysis (DEA) approach within a stochastic framework. The proposed bilevel DEA model takes into account stochastic conditions and optimizes centralized resource allocation and target setting, imposing lower bounds on the efficiencies of all DMUs affiliated to the organization. Consequently, the total input consumption is minimized, and the total output production is maximized while considering additional bounds and availability constraints for inputs. In the proposed bilevel model, uncertainty is introduced through the upper level (leader) problem that attempts to maximize organizational effectiveness, while in the lower level (follower) problem, the efficiency of the subordinate DMUs is evaluated. A solution methodology for the bilevel network DEA-based model is presented and numerical results are obtained using data from the literature. The obtained results are compared with those published in other case studies for centralized resource allocation DEA models. Full article

Presented in this paper is a trigonometrically fitted scheme based on a class of improved hybrid method for the numerical integration of oscillatory problems. The trigonometric conditions are constructed through which a third algebraic order scheme is derived. Numerical properties of the scheme are analysed. A numerical experiment is conducted to validate the scheme. Results obtained reveal the superiority of the scheme over its equals in the literatur.e Full article

In this paper, we consider a generalized Mittag-Leffler (ML)-type function and establish several integral formulas involving Jacobi and related transforms. We also establish some of the composition of generalized fractional derivative formulas associated with the generalized Mittag-Leffler (ML)-type function. Additionally, certain special cases of generalized fractional derivative formulas involving the Mittag-Leffler (ML)-type function are corollarily presented. Full article

Quasars are astronomical star-like objects having a large ultraviolet flux of radiation accompanied by generally broad emission lines and absorption lines in some cases found at large redshift. The used data is extracted from the Veron Cetti Catalogue of AGN and Quasar. The objective of this work is to partition the quasar based on their spectral properties using multivariate techniques and classify them with respect to the obtained clusters. Performing the K-means partitioning method, two robust clusters were obtained with cluster sizes 39,581 and 129,377. The percentage of misclassification observed based on the obtained clusters considering a multivariate classification technique and machine learning classification algorithm, i.e., linear discriminant analysis and XG-Boost, respectively. The linear discriminant analysis and XG-Boost evaluated a misclassification of around 0.84 and 0.15%, respectively. Additionally, a heuristic literature-based categorization subject to redshift yielded an accuracy of around 96 %. This gives us cross-validating arguments about the astronomical data, that machine learning algorithms might perform on par with conventional multivariate techniques, if not better. Full article

The number of software failures, software reliability, and failure rates can be measured and predicted by the software reliability growth model (SRGM). SRGM is developed and tested in a controlled environment where the operating environment is different. Many SRGMs have developed, assuming that the working and developing environments are the same. In this paper, we have developed a new SRGM incorporating the imperfect debugging and testing coverage function. The proposed model’s parameters are estimated from two real datasets and compared with some existing SRGMs based on five goodness-of-fit criteria. The results show that the proposed model gives better descriptive and predictive performance than the existing selected models. Full article

In this paper, we present a two-component Weibull mixture model. An important property is that this new model accommodates bimodality, which can appear in data representing phenomena in some heterogeneous populations. We provide statistical properties, such as the quantile function and moments. Additionally, the expectation-maximization (EM) algorithm is used to find maximum-likelihood estimates of the model parameters. Further, a Monte Carlo study is carried out to evaluate the performance of the estimators on finite samples. The new model’s relevance is shown with an application referring to the vote proportion for the Brazilian presidential elections runoff in 2018. The proportion of votes is an important measure in analyzing electoral data. Since it is a variable limited to the unitary interval, unit distributions should be considered to analyze its probabilistic behavior. Thus, the introduced model is suitable for describing the characteristics detected in these data, such as the asymmetric behavior, bimodality, and the unit interval as support. In the application, the superiority of the proposed model is verified when comparing the fit with the two-component beta mixture models. Full article

The present work proposes a new class of model for random variables with support in the positive real line, this model explains the conditional quantile and is an alternative for modeling data that indicate asymmetric behavior and heavy tails. We present a new autoregressive moving average model based on the $\tau$–th quantile of the Burr XII distribution (BXII-ARMA) since the quantile is less sensitive than the average of heterogeneous populations and also suitable in the presence of outliers. This model makes it possible to model any quantile by a dynamic structure containing autoregressive terms and moving averages, time-varying regressors, unknown parameters, and a link function. The conditional maximum likelihood method is considered to estimate the parameters and build the confidence intervals of the BXII-ARMA model. In addition, the model is adjusted to real data related to the financial market and compared with other competing models. Full article

Solving various real-life problems ultimately requires solving systems of linear equations. However, the parameters involved in such real-life problems may be pervaded with uncertainty, which results in fuzzy parameters rather than crisp parameters. Intuitionistic fuzzy parameters are more suitable for some cases, since they allow us to tackle the feeling of fear or hesitation when making a decision. These are characteristics of human beings that occur when applying knowledge and skills. The intuitionistic fuzzy linear system (IFLS) resulting from real-life problem involves large number of equations and equally large number of unknowns. When IFLS is in matrix-vector form, the resulting coefficient matrix will have a sparse structure, which makes iterative methods necessary for their solution. In this paper, the known Gauss–Seidel and SOR iterative methods for solving linear system of equations are discussed, to the best of our knowledge for the first time, to solve (IFLS). The single parametric form representation of intuitionistic fuzzy numbers (IFN) makes it possible to apply these iterative techniques to IFLS. Finally, a problem of voltage input output in an electric circuit has been considered to show the applicability and the efficiency of these methods. Full article

In this paper, we investigate an intuitionistic fuzzy Poisson equation with uncertain parameters, considering the parameters as intuitionistic fuzzy numbers. We apply a finite difference method to solve the ‘Intuitionistic fuzzy Poisson equation’. The continuity of the membership and non-membership functions (which imply the continuity of the hesitancy function) is used to obtain qualitative properties on regular $\alpha$-cut and $\beta$-cut of the intuitionistic fuzzy solution. The fuzzification of the deterministic $\alpha$-cut and $\beta$-cut solutions obtained lead to the intuitionistic fuzzy solution. Finally, an example is presented to illustrate the proposed methodology, as well as to show a graphical representation of its corresponding intuitionistic fuzzy solution. Full article

In this paper, the desymmetrized PSL(2, Z) group is studied. The Fourier coefficients of the non-holomorphic one-cusp Eisenstein series expansion are summed, and as a further result, a new dependence on the Euler’s $\gamma$ constant is found. The congruence subgroups of the desymmetrized $PSL(2,\mathbf{Z})$ are scrutinized, and the related structures are investigated. A ‘square-box’ one-cusp congruence subgroup is constructed. New leaky tori are constructed. Full article

The definition and description of the dynamics of a predator–prey system are some of the fundamental problems of population biology. Since 1925, several models have been introduced. Although they are highly effective, most of them neglect certain relevant criteria such as the spatial and temporal distribution of the studied species. We introduced these criteria by coupling two models designed initially for collective dynamics. The first is for predator mobility and is a Vicsek-type model, and the second is a Brownian particle (BP) model for prey. We observed, as occurs in the classical models, periodic cycles of the densities of predators and prey. In this case, the period of oscillations depends on the collective dynamics parameters. Full article

In this article, we study the growth properties of solutions of homogeneous linear differential–difference equations in the whole complex plane $\sum _{j=0}^n{A}_j\left(z\right)f^{\left(j\right)}\left(z+c_j\right)=0,n\in {\mathbb{N}}^{+},$ where $c_j,j=0,...,n$ are complex numbers, and $A_j\left(z\right),j=0,\dots ,n$ are entire functions of the same order. Full article

Recent mathematical models of reliability computer systems and telecommunication networks are based on distributions with heavy tails. This paper falls into the category of exploring the classical models with heavy tails: Gnedenko–Weibull, Burr, Benktander distributions. The moment’s asymptotics for residual time have been derived especially for there heavy-tailed distributions. A simulation study is presented to give a practice characterization of the distributions with heavy tails. Full article

This article discusses the class of Periodic Generalized Poisson Integer-Valued Generalized Autoregressive Conditional Heteroscedastic $\left(PGPINGARCH\right)$ models. The model, in addition to properly capture the periodic feature in the autocovariance structure, encompasses different types of dispersions, with this conditional marginal distribution. The main theoretical properties of this model are developed, in particular, the first two moment periodically stationary conditions, while the closed form of these moments are derived. Moreover, the existence of the higher order moment and their closed forms are established. The periodic autocovariance structure is studied. The estimation is done by the Yule Walker and the Conditional Maximum Likelihood methods and their performance is shown via an simulation study. Moreover, an application on Campylobacteriosis time series is provided, which indicates that the proposed models performs better than other models in the literature. Full article

The primary motivation of this article is to introduce the definition of a strongly belonging element of a brace, presenting some results concerning the case where I acts as an ideal of a brace, $(A,+,\circ )$. We find that an element $a\in I$ acts as strongly belonging element of I when $a+b$ yields a for all b in I. Full article

Quantum–classical mechanics and the Franck–Condon principle related to quantum mechanics are discussed as two alternative theoretical approaches to molecular optical spectroscopy. The statement of the problem is connected with the singularity of quantum mechanics in describing the joint motion of electrons and nuclei in the transient state of “quantum” transitions. This singularity can be eliminated by introducing chaos into the transient state. Quantum mechanics itself, supplemented by chaos (dozy chaos), is called quantum–classical mechanics. Using the simplest example of quantum transitions, it is shown that the results of quantum–classical mechanics in the case of strong dozy chaos correspond to the physical picture based on quantum mechanics and the Franck–Condon principle. The same chaos can be strong for small molecules in standard molecular spectroscopy and simultaneously weak in the photochemistry and nanophotonics of large molecules, where quantum mechanics no longer works. To describe the chaotic dynamics of the transient state, it is necessary to apply quantum–classical mechanics. Thus, the erroneous Franck–Condon physical picture of molecular “quantum” transitions is workable from a practical point of view as long as we are dealing with sufficiently small molecules, just as the erroneous geocentric picture of the world was workable until we went out into outer space. Full article

In this article, we developed the idea of q-time scale calculus in quantum geometry. It includes the q-time scale integral operators and${∆}_q$-differentials. It analyzes the fundamental principles which follow the calculus of q-time scales compared with the Leibnitz–Newton usual calculus and have few crucial consequences. The ${∆}_q$-differential reduced method of transformations was proposed to work out on partial ${\mathsf{\Delta }}_q$-differential equations in time scale. With easily computable coefficients, the result is calculated in the version of a power series which is convergent. The performance and effectiveness of the proposed procedure are also illustrated, and Matlab software is applied for calculation with the support of some fascinating examples. It changes when $\sigma \left(t\right)=t$ and q = 1; then, the solution merges with usual calculus for the mentioned initial value problem. The finding of the present work is that the ${\mathsf{\Delta }}_q$-differential transformation reduced method is convenient and efficient. Full article

This paper deals with fractional order three-phase-lag (TPL) thermo-elasticity in a micropolar thermoelastic half space medium with voids. The subsequent non-dimensional coupled equations are solved by using the normal mode analysis and eigenvalue approach methods. By doing numerical computations of the physical fields for a substance that resembles a magnesium crystal in the presence of an electromagnetic field, the issue is proven to exist. The effect of the fractional order, the phase lags on the components of temperature, displacement, the stress, and changes in volume fraction field have been depicted graphically. Additionally, a graphic comparison of several types of models employing phase delays and the influence of the magnetic field is displayed. Full article

We define the class of extended $b_v\left(s\right)$-metric spaces by replacing the real number $s\ge 1$ with a strictly increasing continuous function $\varphi$ in the definition of a $b_v\left(s\right)$-metric space. Also, we presented an example for this newly introduced space and exhibited that in a particular situation, the class of extended $b_v\left(s\right)$-metric spaces reduces to the class of $b_v\left(s\right)$-metric spaces. Afterwards, we establish a fixed point theorem which ensured the existence of a fixed point for the self-map satisfying the Banach contractive condition in the context of this newly defined space. Moreover, we compared the proved result with the existing fixed point theorems in the literature. Full article

We consider a queuing system ${\mathit{GI}}^{\nu }\left|M\right|1|\infty$ with arrival of customers in batches, general renewal arrivals, exponential service times, single service channels and an infinite number of waiting positions, where customers are serviced in the order of their arrival. In the stationary case, new forms of the probability generating functions of the number of clients in the system are derived. These new forms are written in terms of the p.g.f. of the tail distribution function of the number of customers per group and of the p.g.f. of an embedded discrete time homogeneous Markov chain. In a queuing system with a batch Poisson arrival flow $M_{\lambda }^{\nu }|M_{\mu }\left|1\right|\infty$, the number of customers in the system can be obtained from the normalized tail distribution. Full article

We offer a new asymptotic expansion with an explicit remainder estimate in the central limit theorem. The results obtained are essentially based on new forms of asymptotic expansions in the central limit theorem. We also present a more accurate estimation of the CLT-expansions remainder which is rigorously proved and backed up numerically. It is shown that our approach can be used for further refinement of allied asymptotic expansions. Full article

In this study, we have dealt with a scheduling problem that has not been studied enough: the parallel-flow shop-scheduling problem. Its difficulty lies in the fact that it consists of two sub-problems: the assignment of jobs to workshops and the scheduling of these jobs once assigned. Due to the complexity of the research problem, we propose a hybridization of two well-known optimization algorithms, a bio-inspired meta-heuristic algorithm (Particle Swarm Optimization—PSO) and a local search algorithm (tabu search, TS), with the aim of minimizing the maximum execution time of all jobs within constraints. The purpose of this hybridization is to combine the strengths of the two methods in order to obtain more efficient results than those achieved by classic methods. The concept of the proposed method is to start by generating a set of near-optimal solutions by the PSO meta-heuristic algorithm. Then, the TS algorithm refines and improves these solutions in order to attain the optimal solution. Full article